Rings and Principal Ideals : Left and Right Ideals
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Show that if R is a ring with identity element and x is an element in R, then
Rx = {rx: r in R} is the principal left ideal generated by x. Similarly,
xR = {xr: r in R} is the principal right ideal generated by x.
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Solution Summary
Left and right ideals are investigated in the solution that is detailed and well presented.
Solution Preview
First, I show that Rx is a subring of R.
For any r,s in R, rx,sx are in Rx, then
rx-sx=(r-s)x is in Rx
rx*sx=(rxs)x ...
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